Answer: 1) In 6 ways the girls can fill the roles of a grandmother, mother, and daughter.
2) A permutation would be used to solve this problem
Step-by-step explanation:
Permutation is an arrangement of the elements of a list into a one to one correspondence with itself, where as a combination is a collection of things in which order doesn't matter at all.
In the given situation there are three girls named Matilda, Tanya and Renee are auditioning for a play. The girls have to fill the roles of a grandmother, mother, and daughter that means no girl can take two roles or no two girls can 1 role i.e. repetition is not allowed so by permutation ,
the number of ways the girls can fill the roles=[tex]\frac{n!}{(n-r)!}=\frac{3!}{(3-3)!}=3!=6[/tex],where n is the total roles and r is the number of girls.
Therefore, in 6 ways the girls can fill the roles of a grandmother, mother, and daughter.
Using arrangements, it is found that the girls can fill the roles in 6 ways.
In this question, we have 3 people for 3 roles, that is, the same number of people and roles, thus, the arrangements formula is used.
The number of possible arrangements of n elements is the factorial of n, that is:
[tex]A_{n} = n![/tex]
In this problem, 3 people for 3 roles, thus [tex]n = 3[/tex], and:
[tex]A_{3} = 3! = 6[/tex]
The girls can fill the roles in 6 ways.
A similar problem is given at https://brainly.com/question/24648661
